I mean, Jeff has already stated he isn't trying to compete with Google. So why have a local site search anyway? Changing the form action value (or letting me choose between SO's and Google's) wouldn't be a drastic change and it would save me from having to open up a new tab, type what I'm looking for and append site:stackoverflow.com to the end.

I would actually suggest that you take a look at setting up a Google Custom Search Engine (CSE) and then you can base you searches on as many (or as little) sites as you want at a single time. Then you could even make that search engine your default search method.